The commentary by Govindaraja throws some light in this respect. It says:
सीतां धनुर्भङ्गकाल इति भाव:।
Sita at the the time of the breaking of the bow, such is the indication.
The simple answer being Shri Rama would’ve given marrying Sitaji, in favour of Bharata at the time of the breaking of the bow despite himself being the one to fulfill Janaka’s vow. To get a better understanding and building of a context read below:
In Shri Rama’s discussion with Kaikeyi, convincing her that he will go to the forest, he says:
हितेन गुरुणा पित्रा कृतज्ञेन नृपेण च। नियुज्यमानो विस्रब्ध: किं न कुर्यामहं प्रियम्॥५॥
अहं हि सीतां राज्यं च प्राणानिष्टान् धनानि च। हृष्टो भ्रात्रे स्वयं दद्यां भरतायाप्रचोदित:॥७॥
किं पुनर्मनुजेन्द्रेण स्वयं पित्रा प्रचोदित:। तव च प्रियकामार्थं प्रतिज्ञामनुपालयन्॥८॥
The king is my guru, well-wisher, father and acknowledges my deeds (grateful to me). On being ordered by him, which such deed, dear to him shall I not to confidently without doubt? .5.
On being told only by you also, I would gladly give the kingdom, Sita, my dear life and wealth for my brother Bharata. 7.
Then, in such a case, if the king, my father, himself orders me and that too for something dear to you, why then will I not follow the promise (of the king)? .8.
Explanation: The above lines have been uttered by Shri Rama as a mark of respect for his father and mother (Kaikeyi). As said by Sitaji to Anasuya, Shri Rama has great respect for his elders and treats Kaikeyi in the same respectful fashion as he treats Kausalya. In this conversation he is trying to convince Kaikeyi that leave the king, but he has so much respect for even Kaikeyi that he would give up all things beloved to him on her bidding and similarly he would willingly go the forest. Among these beloved things he says at the time of the breaking of the bow in the Swayamvar, despite he being the one to break it, had Kaikeyi even bid Shri Rama to not marry Sitaji and let Bharata be the groom instead, he would’ve gladly given up marrying her in favour of Bharata. This statement shows the amount of respect he had for his elders, even Kaikeyi, though she may have been being unfair.
Note: the above translation of Sarga 19 is based on Gita Press Gorakhpur which itself is very authentic and generally bases it on thorough research.